Answer:
[tex]y=3x+2[/tex]
Step-by-step explanation:
To find the equation, use the slope-intercept formula:
[tex]y=mx+b[/tex]
m is the slope and b is the y-intercept. Now, it'll really help to draw a line through the points, connecting them. If you look at point (0,2), we can see that this is the y-intercept (where a point sits on the y-axis when x=0). You can insert this into the equation by taking the y value:
[tex](0,2)\\y=mx+2[/tex]
Now, take any two points to find the slope. To make it easier, I'll use (1,5) and (0,2). Use the slope formula for when you know two points:
[tex]\frac{y(2)-y(1)}{x(2)-(x1)} =\frac{rise}{run}[/tex]
Rise over run is the change in the y-axis over the change in the x-axis. Insert values:
[tex](1(x1),5(y1))\\(0(x2),2(y2))\\\\\frac{2-5}{0-1}[/tex]
Solve:
[tex]\frac{2-5}{0-1}=\frac{-3}{-1}[/tex]
Since both are negative, the result is a positive:
[tex]\frac{-3}{-1}=\frac{3}{1} =3[/tex]
Insert this into the equation as m, the slope:
[tex]y=3x+2[/tex]
Done.
