Question

-4x + 7 = 2y - 3 y-intercept: x intercept:

Answer 1

Answer:

x-intercept: $\bigg(\frac{5}{2}, \:0\bigg)$

y-intercept: $(0,\:5)$

Step-by-step explanation:

To find the x-intercept, substitute in $0$ for $y$ and solve for $x$.

$-4x + 7 = 2y - 3$

$-4x+7=2\left(\bold{0}\right)-3$

Simplify 2(0):                                          $-4x+7=2\cdot \:0-3$

Subtract 0 - 3 = -3:                         $-4x+7=-3$

Subtract 7 from both sides:          $-4x+7-7=-3-7$

Simplify:                                         $-4x=-10$

Divide both sides by -4                $\frac{-4x}{-4}=\frac{-10}{-4}$

$\bold{x=\frac{5}{2}}$

To find the y-intercept, substitute in $0$ for $x$ and solve for $y$.

$-4x + 7 = 2y - 3$

$-4(\bold{0})+7=2y-3$

Switch sides:                               $y-3=-4\left(0\right)+7$

Simplify -4(0):                              $2y-3=-0+7$

Add 3 to both sides:                  $2y-3+3=7+3$

Simplify:                                      $2y=10$

Divide both sides by 2:             $\frac{2y}{2}=\frac{10}{2}$

$\bold{y=5}$