Answer:
y = 2x - 3
Explanation:
The slope-intercept form of the equation of a line is generally given as;
[tex]y=mx+b[/tex]where m = the slope of the line
b = the y-intercept of the line
The slope(m) of the line can be determined using the below formula;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Given the points (3, 3) and (4, 5), so our x1 = 3, x2 = 4, y1 = 3, and y2 = 5.
Let's substitute these values into our slope formula and solve for m;
[tex]m=\frac{5-3}{4-3}=\frac{2}{1}=2[/tex]Let's go ahead and use point (3, 3) where x = 3 and y = 3 with slope(m) = 2 to determine the y-intercept(b);
[tex]\begin{gathered} y=mx+b \\ 3=2(3)+b \\ 3=6+b \\ b=3-6 \\ b=-3 \end{gathered}[/tex]We now have m = 2 and b = -3, therefore the required equation of a line can be written as;
[tex]y=2x-3[/tex]