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.