Write the slope-intercept form of the equation of the line through the given point with the given slope - Show Work and Explain

Question

Through: (1,-3), slope = -7

Answer 1

To find the slope-intercept form (y=mx+b), you can start with the point-slope form of a line, which is:

y−y1​=m(x−x1​)

Here, the given point is (x1​,y1​) = (1, -3) and the slope m is -7.

Substitute these values into the point-slope formula: y−(−3)=−7(x−1)

Simplify the equation to convert it to slope-intercept form: y+3=−7x+7

Subtract 3 from both sides to isolate y:

y=−7x+7−3

y=−7x+4

Answer 2

We have a point and a slope, so we can use the point slope formula:

y - y₁ = m(x - x₁)

Put in the coordinates and slope:

y - (-3) = -7(x - 1)

2 subtraction signs make a plus and distribute:

y + 3 = -7x + 7

Subtract 3 from both sides:

y = -7x + 4