Question

What is the slope-intercept form of the line passing through `(3,0)` and `(-4, 1)`?

Answer 1

`y=-1/7x+3/7`

Explanation:

The equation of straight line passing through the points `(x_1, y_1)\equiv(3, 0)` & `(x_2, y_2)\equiv(-4, 1)` is given as follows

`y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)`

`y-0=\frac{1-0}{-4-3}(x-3)`

`y=-1/7(x-3)`

`y=-1/7x+3/7`

Above equation of line is the slope-intercept form: `y=mx+c`

Answer 2

`y=-1/7*x+3/7`

Explanation:

After using slope formula for known 2 points,

`m=(1-0)/(-4-3)=1/(-7)=-1/7`

After using formula for known slope and a point,

`y-0=-1/7*(x-3)`

`y=-1/7*x+3/7`

Answer 3

`y=-1/7x+3/7`

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)=(3,0)" and "(x_2,y_2)=(-4,1)`

`m=(1-0)/(-4-3)=1/(-7)=-1/7`

`y=-1/7x+blarrcolor(blue)"is the partial equation"`

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

`"using "(3,0)" then"`

`0=-3/7+brArrb=0+3/7=3/7`

`y=-1/7x+3/7larrcolor(red)"in slope-intercept form"`