Question
Given that the coordinate (3, 4) lies on the line y = 3x + c calculate the y-intercept of the straight line.
Hint:
We can calculate the y-intercept of the line from the slope-intercept form of the equation of a line. We are given the equation in that form and we are given a point that satisfies this equation. We use this point to find the value of c from the given equation. This will help us find the y- intercept.
The correct answer is: the y-intercept is -5.
Step by step solution:
The given equation of the line is
y = 3x + c
Comparing with the slope intercept form of the equation of a line,
y = mx + c
We get that denotes the y intercept of the line in the equation y = 3x + c
As every point that lies on the line satisfies the equation of the line, we get the point (3, 4) satisfies the equation y = 3x + c
Thus, we have
4 = 3 × 3 + c
Simplifying, we get
4 = 9 + c
Subtracting 9 on both sides, we get
c = 4 - 9 = -5
Thus, the value of c is -5
Hence, the y-intercept is -5.
Comparing with the slope intercept form of the equation of a line,
We get that denotes the y intercept of the line in the equation y = 3x + c
As every point that lies on the line satisfies the equation of the line, we get the point (3, 4) satisfies the equation y = 3x + c
Thus, we have
Simplifying, we get
Subtracting 9 on both sides, we get
Thus, the value of c is -5
Hence, the y-intercept is -5.
The student needs to remember all the different forms of equation of a line and what each term and notation signifies in the equation.
We can find the slope and y-intercept directly from the general form of the equation too; slope = 
and y-intercept = 
, where the general form of equation of a line is ax + by + c = 0.
