Question

what is the equation off the straight line with gradient 7 that passes through(2,6).give your answer in the form y=mx+c, where m and c are integers or fractions in their simplest forms

Answer 1

y = 7x - 8

Explanation:

We're asked to find the equation of a line, given that:

⇒ The line has a gradient of 7.

⇒ The line passes through the point (2,6).

With this data, we can use the point-slope formula.

⇒
`\boldsymbol{y-y_1=m(x-x_1)}`

Substitute the values:

⇒
`\longmapsto\boldsymbol{y-6=7(x-2)}\\\\\longmapsto\boldsymbol{y-6=7x-14}\\\\\longmapsto\boldsymbol{y=7x-14+6}\\\\\longmapsto\boxed{\boldsymbol{y=7x-8}}`

Therefore, our equation, in slope-intercept form, is y = 7x - 8.

Answer 2

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

`(\stackrel{x_1}{2}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 7 \\\\\\ \begin{array}c \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{7}(x-\stackrel{x_1}{2}) \\\\\\ y-6=7x-14\implies {\Large \begin{array}{llll} y=7x-8 \end{array}}`