Question

Make a table of values, and sketch the graph of the equation.

$3x-5y=30$

Short answer

The graph of the equation$3x-5y=30$ is provided below.

Step-by-step solution

Step 1. Apply the concept of slope-intercept form.

Equation of line in slope intercept form is expressed below.

$y=mx+c$

Where m is the slope and c is the intercept of y-axis.

Step 2. Write the equations in slope-intercept form.

Consider the equation $3x-5y=30$.

Rewrite the equation in form of slope-intercept form.

Subtract both sides by 3x and then divide by $-5$.

localid="1643625051572" $$\begin{gathered} 3x-5y-3x=30-3x \\ -5y=-3x+30 \\ y=\frac{3}{5}x-6 \end{gathered}$$

Now, the equation is in the form $y=mx+c$. Here slope m of the line is$\frac{3}{5}$ and intercept of y-axis cis $-6$.

Step 3. Construct a table of values.

Consider real values for x and corresponding to it find the values of y.

$\begin{array}{ccc}x& y=\frac{3}{5}x-6& \left(x,y\right)\\ -1& -6.6& \left(-1,-6.6\right)\\ 0& -6& \left(0,-6\right)\\ 1& -5.4& \left(1,-5.4\right)\\ 2& -4.8& \left(2,-4.8\right)\\ 10& 0& \left(10,0\right)\end{array}$

Step 4. Graph the equation.

Plot the ordered pairs on the Cartesian plane to obtain the graph of the equation $3x-5y=30$.