Graph 1<=y<=5 y>=4x-3 y>=-4x-3 f(x,y)=-8x+y

$1 \leq y \leq 5$ $y \geq 4 x - 3$ $y \geq - 4 x - 3$ $f (x, y) = - 8 x + y$

Step 1

Graph $1 \leq y \leq 5$ .

$1 \leq y \leq 5$

Step 2

Graph $y \geq 4 x - 3$ .

Use the slope-intercept form to find the slope and y-intercept.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = 4$

$b = - 3$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $4$

y-intercept: $(0, - 3)$

Slope: $4$

y-intercept: $(0, - 3)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $4 x - 3$ .

$y \geq 4 x - 3$

Step 3

Graph $y \geq - 4 x - 3$ .

Use the slope-intercept form to find the slope and y-intercept.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - 4$

$b = - 3$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- 4$

y-intercept: $(0, - 3)$

Slope: $- 4$

y-intercept: $(0, - 3)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- 4 x - 3$ .

$y \geq - 4 x - 3$

Step 4

Plot each graph on the same coordinate system.

$1 \leq y \leq 5$

$y \geq 4 x - 3$

$y \geq - 4 x - 3$

$f (x, y) = - 8 x + y$

Step 5