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The equation of a line is written in the form y=mx+b. “m” is the slope and “b” is the y-intercept. To find the slope, use the distance formula. The distance formula is Y2-Y1/X2-X1. You can use any two points on the graph but I will use (0,4) and (3,6).

6-4/3-0

2/3

The slope is 2/3. To find the y-intercept, look at the graph and find the where the line crosses the y-axis. The y-intercept in 4. So, the equation of this line is y=2/3x+4.

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SEMSEE45GO SEMSEE45GO · Answer 2

Answer:

[tex]y=\boxed{\dfrac{2}{3}}\:\:x+\boxed{4}[/tex]

Step-by-step explanation:

Slope-intercept form of a linear equation:

[tex]y = mx + b[/tex]

where:

m is the slope
b is the y-intercept

To find the slope of the given line, define two points on the line:

[tex](x_1,y_1)=(-6,0)[/tex]
[tex](x_2,y_2)=(0,4)[/tex]

Substitute the two defined points into the slope formula and solve for m:

[tex]\implies \textsf{slope}\:(m)=\dfrac{4-0}{0-(-6)}=\dfrac{4}{6}=\dfrac{2}{3}[/tex]

The y-intercept is y-value of the point at which the lines crosses the y-axis. From inspection of the graph, the y-intercept is 4.

Therefore, substitute the found slope and y-intercept into the slope-intercept formula to create the equation of the given line:

[tex]\implies y=\dfrac{2}{3}x+4[/tex]

To learn more about slope-intercept form here:

https://brainly.com/question/27926846