Question

(a) Write the point–slope form of a function that has a slope of 3- 5 and passes through the point (6,1).

Answer 1

The question illustrates linear equation

• The equation in point slope form is: $\mathbf{ y - 1 = \frac 35 (x - 6)}$
• The equation in slope intercept form is: $\mathbf{ y = \frac 35x - \frac{13}5}$

The given parameters are:

$\mathbf{m = \frac 35}$ --- the slope

$\mathbf{(x_1,y_1) = (6,1)}$ -- the point it passes through

(a) The equation in point slope form

This is represented as:

$\mathbf{ y - y_1 = m(x - x_1)}$

Substitute known values

$\mathbf{ y - 1 = \frac 35 (x - 6)}$

So, the equation in point slope form is: $\mathbf{ y - 1 = \frac 35 (x - 6)}$

(a) The equation in slope intercept form

In (a), we have:

$\mathbf{ y - 1 = \frac 35 (x - 6)}$

Open brackets

$\mathbf{ y - 1 = \frac 35x - \frac{18}5}$

Add 1 to both sides

$\mathbf{ y = \frac 35x - \frac{18}5 + 1}$

Take LCM

$\mathbf{ y = \frac 35x + \frac{-18 + 5}5}$

$\mathbf{ y = \frac 35x + \frac{-13}5}$

$\mathbf{ y = \frac 35x - \frac{13}5}$

Hence, the equation in slope intercept form is: $\mathbf{ y = \frac 35x - \frac{13}5}$

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