Question

Write an equation of the line that passes through the point and has the given slope. Use slope-intercept form. $$ (-4,3), m=1 $$

Short answer

The equation of the line in slope-intercept form that passes through the point (-4, 3) and has slope m = 1 is y = x + 7.

Step-by-step solution

Plug in The Slope

For the line equation in slope-intercept form, y = mx + b, we are given the slope 'm' as 1. So the line equation becomes y = 1x + b or simply y = x + b.

Plug in The Given Point

We have the given point (-4, 3) which means at x = -4, y = 3. Substitute these values into the line equation from Step 1. This gives 3 = -4 + b.

Solve for the y-intercept, 'b'

To find the value of 'b', add 4 to both sides of the equation from Step 2: 3 = -4 + b becomes 3 + 4 = b. Simplify to find b = 7.

Write the Final Equation

Substitute b = 7 into the line equation from Step 1, resulting in the final line equation y = x + 7.