Question

In a standard coordinate plane, what is the y-intercept of a line that passes through the points (3,17) and (5, 29)?

Answer 1

`"y-intercept "=-1`

Explanation:

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`"to calculate m use the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(3,17)" and "(x_2,y_2)=(5,29)`

`rArrm=(29-17)/(5-3)=12/2=6`

`rArry=6x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute either of the 2 given points into"`
`"the partial equation"`

`"using "(3,17)" then"`

`17=18+brArrb=17-18=-1`

`rArry=6x-1larrcolor(red)"in slope-intercept form"`

`rArrb=" y-intercept "=-1`