Question

A line passes through (9,-9) and (10,-5).

a. Write an equation for the line in point-slope form.
b. Rewrite the equation in standard form using integers.
y-9 = 46% + 9); -4x + y = 45
y + 9 = 4(x + 9); -4% + y = -45
Y + 9 = 4(-9); -4x + y = -45
y - 9 = 40%-9); -4% + y = 45

Answer 1

y + 9 = 4(x - 9); -4x + y = -45

Explanation:

According to the Point-Slope Formula [y - y₁ = m(x - x₁)], all the negative symbols give the OPPOSITE terms of what they really are, so put the coordinates into their correct positions, depending on the signs. In the equation, there is a 9 in it [-(-9) = 9], according to the formula. By the way, this is its y-coordinate. The x-coordinate is 9, which is normal, according to the formula (see part of above answer in parentheses). So now, this is how your work will look:

y + 9 = 4x - 36 [Point-Slope Form]↷

- 9 - 9

----------------

y = 4x - 45 [Slope-Intercept Form]↷

-4x -4x

------------

-4x + y = -45 [Standard Form]

Here we are at this second equation.

I am joyous to assist you anytime.

Answer 2

`\bf (\stackrel{x_1}{9}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{-5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-5-(-9)}{10-9}\implies \cfrac{-5+9}{1}\implies 4 \\\\\\ \begin{array} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-9)=4(x-9)\implies y+9=4(x-9) \\\\\\ y+9=4x-36\implies y=4x-45\implies \stackrel{\textit{standard form}}{-4x+y=-45}`

just a quick note

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

now, however the inappropriate choices here, do have it with a negative "x".