Q60. - Algebra 2

Question

4. Find the x-intercept and the y-intercept of the graph of each equation. Then, graph the equation. (Lesson 2-2)

60. $\mathbf{y}=\mathbf{7}\mathbf{x}$

Step-by-Step Solution

Answer

The x-intercept and the y-intercept of the graph of the given equation are both 0. Thus, the graph passes through the origin. The graph of the given equation is given as follows:

Step 1 – State the concept

The x-intercept is the value of x when $y=0$. Similarly, the y-intercept is the value of y when $x=0$.

Step 2 – List the given data

The given equation is $y=7x$.

Step 3 – Find the intercepts

Solving for x-intercept,

 

$y=7x$   (Given equation)

 

$0=7x$   (Put $y=0$ in the given equation)

 

$7x=0$   (Simplify)

 

$\frac{7x}{7}=\frac{0}{7}$  (Divide both sides by 7)

 

$x=0$   (Simplify)

 

So, the x-intercept is $0$ and the graph crosses the x-axis at the point $\left(0,0\right)$.

 

Similarly, solving for y-intercept,

 

$y=7x$   (Given equation)

 

$y=7\left(0\right)$  (Put $x=0$ in the given equation)

 

$y=0$   (Simplify)

 

So, the y-intercept is $0$ and thus the graph crosses the y-axis at the point $\left(0,0\right)$.

Step 4 – Graph the equation

Graphing the given equation using the obtained ordered pair and the slope,