Question

Write an equation in point-slope form and in slope-intercept form. A line passes through (1, -5)* and (-3, 7) Write an equation for the line in point-slope form and rewrite the equation in slope-intercept form *this is the first point (x1, y1) plz show work

Answer 1

Point-slope form:

y - y₁ = m(x - x₁)

You need to find "m" which is the slope.

To do so, use the slope formula and plug in the two points:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{7-(-5)}{-3-1}$  

$m=\frac{7+5}{-3-1} =\frac{12}{-4} =-3$

m = -3

(x₁ , y₁) = (1, -5)

Plug this into the equation:

y - y₁ = m(x - x₁)

y - (-5) = -3(x - 1)

y + 5 = -3(x - 1)      

Slope-intercept form:

y = mx + b       "m" is the slope, "b" is the y-intercept

In order to get the equation from point-slope form to slope-intercept form, isolate/get the "y" by itself.

y + 5 = -3(x - 1)   First distribute/multiply -3 into (x - 1)

y + 5 = -3x + 3      Subtract 5 on both sides

y = -3x - 2