Find the x and y Intercepts y=|4x-7|+2

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

Find the x-intercepts.

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

$0 = | 4 x - 7 | + 2$

Solve the equation.

Rewrite the equation as $| 4 x - 7 | + 2 = 0$ .

$| 4 x - 7 | + 2 = 0$

Subtract $2$ from both sides of the equation.

$| 4 x - 7 | = - 2$

There is no value of $x$ that makes the equation be true since an absolute value can never be negative.

No solution

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

x-intercept(s): $None$

Find the y-intercepts.

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

$y = | 4 (0) - 7 | + 2$

Simplify $| 4 (0) - 7 | + 2$ .

Simplify each term.

Multiply $4$ by $0$ .

$y = | 0 - 7 | + 2$

Subtract $7$ from $0$ .

$y = | - 7 | + 2$

The absolute value is the distance between a number and zero. The distance between $- 7$ and $0$ is $7$ .

$y = 7 + 2$

Add $7$ and $2$ .

$y = 9$

y-intercept(s) in point form.

y-intercept(s): $(0, 9)$

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 9)$