Question

Give the slope and y - intercept for each of the following equations, then sketch the graph. Give the slope ofany line perpendicular to the given line.5x - 3y = - 15Slope =y - intercept = (0,_ )

Answer 1

Step-by-step explanation

So we must give the slope, the y-intercept, the graph and the slope of a perpendicular line to the line given by the following equation:

`5x-3y=-15`

The equation of a line in slope-intercept form is the following:

`y=mx+b`

Where m is the slope and b is the y-value of the y-intercept. We can try to rewrite the equation given by the question so that it is written in slope-intercept form and we can use it to solve the first part. We can start by substracting 5x from both sides:

`\begin{gathered} 5x-3y-5x=-15-5x \\ -3y=-15-5x \end{gathered}`

Then we can divide both sides by -3:

`\begin{gathered} (-3y)/(-3)=(-15-5x)/(-3) \\ y=(-5x)/(-3)+(-15)/(-3) \\ y=(5)/(3)x+5 \end{gathered}`

So we have m=5/3 and b=5.

In order to sketch the graph of a line we need at least two of its points. We can choose two random x-values and use them to find their corresponding y-values with the equation above. For example, we choose x=0 and x=-3 so we get:

`\begin{gathered} x=0\rightarrow y=(5)/(3)\cdot0+5=5\rightarrow(0,5) \\ x=-3\rightarrow y=(5)/(3)\cdot(-3)+5=-5+5=0\rightarrow(-3,0) \end{gathered}`

So we must draw a line that passes through the points (-3,0) and (0,5).

Finally, the slope of a perpendicular line of a line given by y=mx+b is -1/m. In our case the slope is 5/3 so the slope of a perpendicular line is:

`-(1)/(m)=-(1)/((5)/(3))=-(3)/(5)`

Answers

Slope = 5/3

y-intercept = (0,5)

The graph is:

Slope of a line perpendicular = -3/5