Graph If two lines are parallel and they are defined by the equations, y=4x-5 and y=ax+2 ; what is the value of a ?

If two lines are parallel and they are defined by the equations, $y = 4 x - 5$ and $y = a x + 2$ ; what is the value of $a$ ?

Step 1

Graph $y = 4 x - 5$ .

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 $y = m x + b$ .

$m = 4$

$b = - 5$

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

Slope: $4$

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

Slope: $4$

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

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & - 5 \\ 1 & - 1 \end{array}$

Graph the line using the slope and the y-intercept, or the points.

Slope: $4$

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

$\begin{array}{c} x & y \\ 0 & - 5 \\ 1 & - 1 \end{array}$

Slope: $4$

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

$\begin{array}{c} x & y \\ 0 & - 5 \\ 1 & - 1 \end{array}$

Step 2

Graph $y = a x + 2$ .

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 $y = m x + b$ .

$m = 1$

$b = 2$

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

Slope: $1$

y-intercept: $(0, 2)$

Slope: $1$

y-intercept: $(0, 2)$

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & 2 \\ 1 & a + 2 \end{array}$

Graph the line using the slope and the y-intercept, or the points.

Slope: $1$

y-intercept: $(0, 2)$

$\begin{array}{c} x & y \\ 0 & 2 \\ 1 & a + 2 \end{array}$

Slope: $1$

y-intercept: $(0, 2)$

$\begin{array}{c} x & y \\ 0 & 2 \\ 1 & a + 2 \end{array}$

Step 3

Graph $a$ .

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 $y = m x + b$ .

$m = 1$

$b = 0$

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

Slope: $1$

y-intercept: $(0, 0)$

Slope: $1$

y-intercept: $(0, 0)$

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & 0 \\ 1 & 1 \end{array}$

Graph the line using the slope and the y-intercept, or the points.

Slope: $1$

y-intercept: $(0, 0)$

$\begin{array}{c} x & y \\ 0 & 0 \\ 1 & 1 \end{array}$

Slope: $1$

y-intercept: $(0, 0)$

$\begin{array}{c} x & y \\ 0 & 0 \\ 1 & 1 \end{array}$

Step 4

Plot each graph on the same coordinate system.

$y = 4 x - 5$

$y = a x + 2$

$a$

Step 5

Graph If two lines are parallel and they are defined by the equations, y=4x-5 and y=ax+2 ; what is the value of a ?

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