Question
Determine the equation of the line that passes through ![left parenthesis negative 3 comma negative 6 right parenthesis text and end text left parenthesis 2 comma 34 right parenthesis](data:image/png;base64,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)
Hint:
We are given two points and we need to find the equation of the line passing through them. The equation of a line passing through two points (a, b) and (c, d) is
![fraction numerator y minus d over denominator d minus b end fraction equals fraction numerator x minus c over denominator c minus a end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG0AAAAkCAYAAACDr7TyAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAxVJREFUeNrtm0GEVVEYx6+RZyQxMkZGIq2SRJLMIjGLPOMZbTKL5InWT6LFeJLEaPEWo02LkWQMT2aRMZuMjBZtMkaSxFtlZAxJMpLh9f/4P163e+/ce94599yr78efe88b59xzzj3f+Y77nyAoPrvQUKCUhpPQex2GcjENLekwpGcBuhZR3oAeOmjvEDQPfYd+QS+gx9BdT/2/Cc1FlD/gb4GjMXgEbUG/oWVoJEsFN1hBPwehz9ARyw8re9ZrqM7rw9A9qMvV5osNaKzvvs4XydWEbXBBSP8r0B1oKkslVagdKpOBbDp44GbMipIXZNzjpF2BWryehNYctjXHSDMQspo+9N2PQh1oOObvuykUxxe+aeHVt1uAbeIVdAnaTBFhTMdA+rqTNRQmpds9WtzPbHMWWo8ov8CQ6ZsG95czDts4D72xVZlUdILqODovXYWeR5TPQE89T9gEE6IWn8cVVSYdVngG1aBF6LrDtL4dUS4TecvjhMmL+pLJl4Tudw4SsB7noE82Q8OC4wOuDMpHhsleB1aY9lY9TZjs36uhSZqKiQi22GTmeIDZY4Mr3WgVdLnaXDLG8CDns7fQZehbQtLjkgqfJSprXWJG6YJj3Nv3uEiMz4I1DqJSIiREXNRhKA+nubcoilMGOeArSnHe0qLof+2/hkdFURRFUcqJK1ub2uUc4crWpnY5h7iytaldzhJ52trENDQL3Ye+sj2xGxwtwBgMZGtLwRD7vc025NvacdOK8rS1ydfrDl+IEbbZ8rz6rNjaUrDCxdHrd9t0jPO2tUm9p0JlMlA/PE6aFVvbPswE/9otxOZh9NXexNY2iIUsqt5hj5OW1dZm2neJZuFvlusm4TFvW1tcvdKZNU+TZtXWluGYI9c/TSrK29YWV+/twI2jOQ1WbW0J7ITuJ7iPGqXfedra5pnw9FPhuc1X9mjV1pbAVvC3ganJLD0zedvalpmITPJ+nGV1z+m+NVtbAvJfOE8YFmUfE4/pqmlledra5HxS48TtcbCmA/9Ys7XtwywjW5Pju12Q/isZGE368Q/brjIRKssSXAAAAS90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1yb3c+PG1pPnk8L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1pPmQ8L21pPjwvbXJvdz48bXJvdz48bWk+ZDwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bWk+YjwvbWk+PC9tcm93PjwvbWZyYWM+PG1vPj08L21vPjxtZnJhYz48bXJvdz48bWk+eDwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bWk+YzwvbWk+PC9tcm93Pjxtcm93PjxtaT5jPC9taT48bW8+JiN4MjIxMjs8L21vPjxtaT5hPC9taT48L21yb3c+PC9tZnJhYz48L21hdGg+buMj/QAAAABJRU5ErkJggg==)
The correct answer is: 8x - y + 18 = 0
Step by step solution:
Let the given points be denoted by
(a, b) = (-3, -6)
(c, d) = (2, 34)
The equation of a line passing through two points and is
![fraction numerator y minus d over denominator d minus b end fraction equals fraction numerator x minus c over denominator c minus a end fraction](data:image/png;base64,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)
Using the above points, we have
![fraction numerator y minus 34 over denominator 34 minus left parenthesis negative 6 right parenthesis end fraction equals fraction numerator x minus 2 over denominator 2 minus left parenthesis negative 3 right parenthesis end fraction](data:image/png;base64,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)
Simplifying the above equation, we have
![fraction numerator y minus 34 over denominator 34 plus 6 end fraction equals fraction numerator x minus 2 over denominator 2 plus 3 end fraction](data:image/png;base64,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)
![not stretchy rightwards double arrow fraction numerator y minus 34 over denominator 40 end fraction equals fraction numerator x minus 2 over denominator 5 end fraction](data:image/png;base64,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)
Cross multiplying, we get
5(y - 34) = 40(x - 2)
Expanding the factors, we have
5y - 170 = 40 x -80
Taking all the terms in the left hand side, we have
-40x + 5y - 170 + 80 = 0
Finally, the equation of the line is
-40x + 5y - 90=0
Dividing the equation throughout by(- 5), we get
This is the required equation.
.
The equation of a line passing through two points and is
Using the above points, we have
Simplifying the above equation, we have
Cross multiplying, we get
Expanding the factors, we have
Taking all the terms in the left hand side, we have
Finally, the equation of the line is
Dividing the equation throughout by(- 5), we get
This is the required equation.
.
We can simplify the equation in any other way and we would still reach the same equation. The general form of an equation in two variables is given by a + by + c=0, where a, b, c are real numbers. The student is advised to remember all the different forms of a line, like, slope-intercept form, axis-intercept form, etc