4). Express your Find the equation (in terms of x) of the line through the points ( - 1, – 1) and (2,
answer in slope-intercept form.
4). Express your Find the equation (in terms of x) of the line through the points ( - 1, – 1) and (2,
answer in slope-intercept form.
y = 2x + 17
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
To calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 7, 3) and (x₂, y₂ ) = (- 10, - 3)
m = [tex]\frac{-3-3}{-10+7}[/tex] = [tex]\frac{-6}{-3}[/tex] = 2
y = 2x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 7, 3 ), then
3 = - 14 + c ⇒ c = 3 + 14 = 17
y = 2x + 17 ← equation of line
First, find the slope using the equation m = (y2 - y1)/(x2 - x1) and then once you have it, put the slope into the equation for a line y = mx + b. So now, all that’s left is finding b so use one of the coordinate given to you and plug them in for x and y and solve for b. Once you find b, you just plug it into the equation with m and then you have your equation.
First we find the slope.
Slope or m = [tex]\frac{Y2 - Y1}{X2 - X1}[/tex]
where X1 is the x-coordinate of the first ordered pair and Y1 is the y-coordinate of the first ordered pair. Same applies to X2 and Y2 for the second ordered pair.
m = [tex]\frac{- 4 - (-1)}{1 - (- 2)}[/tex]
m = [tex]\frac{- 4 + 1}{1 + 2}[/tex]
m = [tex]\frac{- 3}{3}[/tex]
m = - 1
Your equation starts as y = - 1x + b or just y = - x + b
Now we plug either ordered pair into the equation and solve for b to get our complete linear function.
- 4 = - (1) + b
- 4 = - 1 + b
- 4 + 1 = b
- 3 = b
Your equation is:
y = - x - 3
From the other question, remember that the general equation for slope-intercept form is y = mx + b, where m = the slope of the equation, b = the y intercept, and x and y are your variables (and the coordinate points on the graph).
This time, we aren't given the value of m, the slope, so we have to find it ourselves. To find slope, use the equation:
[tex]slope = m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
where [tex]x_{2}[/tex] and [tex]y_{2}[/tex] are the x and y values of one coordinate point [tex](x_{2}, y_{2})[/tex], and [tex]x_{1}[/tex] and [tex]y_{1}[/tex] are the x and y values of another coordinate point [tex](x_{1}, y_{1})[/tex]. Since we are given two coordinate points, that means we can find the slope using that equation.
Let's choose (4, -6) as our [tex](x_{2}, y_{2})[/tex] coordinate points and (-1, 4) as our [tex](x_{1}, y_{1})[/tex] coordinate point, but you can switch them around, it doesn't matter! That means [tex]x_{2} = 4[/tex], [tex]y_{2} = -6[/tex], [tex]x_{1} = -1[/tex], and [tex]y_{1} = 4[/tex]. Plug those values into your slope equation to find m:
[tex]slope = m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{-6 - 4}{4 - (-1)} = \frac{-10}{5} = -2[/tex]
That means your slope, m = -2. Now let's go back to our slope-intercept equation y = mx + b and plug m in. Now we have y = -2x + b. Like we did in that last problem, let's find b by plugging in one of our coordinate points! I'll plug in (-1, 4), but you can use (4, -6):
[tex]y = -2x + b\\ 4 = -2(-1) + b\\ 4 = 2 + b\\ b = 2 [/tex]
That means b = 2, so plug that into y = -2x + b to get your final equation:
Your answer is y = -2x + 2.
(3+5)/(2+2) = 8/4 = 2
Y = 2x + b
3 = 2(2) + b, b = -1
Equation: y = 2x - 1