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What is the equation of the line passing through the points( 29 ) and 2) in slope-intercept form?O y-zx-3O y-3x+o y = 2 x - 22O x- x+Mark this and retumSave and ExitNexSubmit

Sagot :

The slope-intercept form is

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

First we find m which is defined as rise / run

[tex]m=\frac{\text{rise}}{\text{run}}=\frac{y_1-y_2}{x_1-x_2}[/tex][tex]\Rightarrow m=\frac{(\frac{11}{12})-(\frac{19}{20})}{(\frac{1}{3})-(\frac{2}{5})}[/tex][tex]m=\frac{1}{2}[/tex]

And finally, we find the y-intercept b from one of the points given.

Let us use the point (1/3, 11/12).

[tex]\frac{11}{12}=\frac{1}{2}(\frac{1}{3})+b[/tex][tex]\frac{11}{12}=\frac{1}{6}+b[/tex][tex]b=\frac{11}{12}-\frac{1}{6}[/tex][tex]b=\frac{3}{4}[/tex]

Hence, the equation of the line in slope-intercept form is

[tex]y=\frac{1}{2}x+\frac{3}{4}[/tex]

which is the second choice in the column.

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