Graph y+3/4x<2 y-1>=2x

$y + \frac{3}{4} x < 2$ $y - 1 \geq 2 x$

Step 1

Graph $y + \frac{3}{4} x < 2$ .

Write in $y = m x + b$ form.

Solve for $y$ .

Combine $\frac{3}{4}$ and $x$ .

$y + \frac{3 x}{4} < 2$

Subtract $\frac{3 x}{4}$ from both sides of the inequality.

$y < 2 - \frac{3 x}{4}$

Rearrange terms.

$y < - \frac{3 x}{4} + 2$

Reorder terms.

$y < - (\frac{3}{4} x) + 2$

Remove parentheses.

$y < - \frac{3}{4} x + 2$

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

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

$m = - \frac{3}{4}$

$b = 2$

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

Slope: $- \frac{3}{4}$

y-intercept: $(0, 2)$

Slope: $- \frac{3}{4}$

y-intercept: $(0, 2)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- \frac{3}{4} x + 2$ .

$y < - \frac{3}{4} x + 2$

Step 2

Graph $y - 1 \geq 2 x$ .

Add $1$ to both sides of the inequality.

$y \geq 2 x + 1$

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 $y = m x + b$ .

$m = 2$

$b = 1$

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

Slope: $2$

y-intercept: $(0, 1)$

Slope: $2$

y-intercept: $(0, 1)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $2 x + 1$ .

$y \geq 2 x + 1$

Step 3

Plot each graph on the same coordinate system.

$y + \frac{3}{4} x < 2$

$y - 1 \geq 2 x$

Step 4

Graph y+3/4x<2 y-1>=2x

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