Question

(1,4), (2,6) (I need these points written in slope-intercept form)

Answer 1

The slope-intercept equation from the two-point form is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`
`x_{1_{}}=1,y_1=4,x_2=2,y_2=\text{ 6}`
`\begin{gathered} y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1) \\ y-\text{ 4 =}(6-4)/(2-1)(x\text{ - 1)} \end{gathered}`
`\begin{gathered} y\text{ - 4 = }(2)/(1)(x-1) \\ y-4\text{ = 2(x-1)} \\ y-4=2x-2 \\ \text{collect like terms} \\ y=2x\text{ -2 +4} \\ y\text{ = 2x + 2} \end{gathered}`

The equation is y = 2x + 2

From y = mx + c

m = 2, c = 2

m is the slope, while c is the intercept on the y-axis

`\begin{gathered} \text{the slope m} \\ m\text{ =}(y_2-y_1)/(x_2-x_1) \end{gathered}`
`\begin{gathered} m\text{ = }(6-4)/(2-1)=(2)/(1)=2 \\ m\text{ = 2} \end{gathered}`