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sasho [114]
3 years ago
11

Determine the slope and y-intercept of a line that passes through the points (-2, 6) and

Mathematics
2 answers:
MrRa [10]3 years ago
8 0

Answer:

y = \frac{-3}{2}x + 3

Step-by-step explanation:

Step 1 - Calculate slope first via the equation:

\frac{y2 - y1}{x2 - x1}

Where x1 and y1 are the coordinates of the first set whereas x2 and y2 are the second set. Plug the variables in:

\frac{6 - (-3)}{-2 - 4} \\\frac{6 + 3 )}{-2 - 4} \\\frac{9}{-6}

Which simplifies to:

\frac{3}{-2}

Now, in the line equation form we know x:

y = mx + c

y = \frac{3}{-2}x + c

Step 2 - Calculate y intercept

Plug the variables of one point into the above equation:

y = \frac{3}{-2}x + c

6 = \frac{3}{-2}(-2) + c

6 = \frac{3}{-2}(-2) + c \\6 = 3 + c\\6 - 3 = c\\c = 3\\

Meaning that the full line equation is:

y = \frac{-3}{2}x + 3

Hope this helps!

Andrei [34K]3 years ago
3 0

Answer:

Y = 3

Step-by-step explanation:

Y = -3/2x +3

Y = -3/2 × 0 + 3

Y = 3

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2 years ago
Derive the equation of the parabola with the focus <br> is (-7,5) and the directrix of y=-11
Volgvan
So, notice, the focus point is at -7, 5, and the directrix is at y = -11.

keep in mind that the vertex is half-way between those two fellows, and the distance from the vertex to either one of them is "p" units, check the picture below.

with that focus point and that directrix, the half-way over the axis of symmetry will be -7, -3, that's where the vertex is at, and notice the distance "p", is 8 units.

since the parabola is opening upwards, "p" is positive 8.

\bf \textit{parabola vertex form with focus point distance}\\\\&#10;\begin{array}{llll}&#10;4p(x- h)=(y- k)^2&#10;\\\\&#10;\boxed{4p(y- k)=(x- h)^2}&#10;\end{array}&#10;\qquad &#10;\begin{array}{llll}&#10;vertex\ ( h, k)\\\\&#10; p=\textit{distance from vertex to }\\&#10;\qquad \textit{ focus or directrix}&#10;\end{array}\\\\&#10;-------------------------------\\\\&#10;\begin{cases}&#10;h=-7\\&#10;k=-3\\&#10;p=8&#10;\end{cases}\implies 4(8)[y-(-3)]=[x-(-7)]^2&#10;\\\\\\&#10;32(y+3)=(x+7)^2\implies y+3=\cfrac{1}{32}(x+7)^2&#10;\\\\\\&#10;y=\cfrac{1}{32}(x+7)^2-3

8 0
3 years ago
HELP ME PLEASE GUYS! :)
UNO [17]

y = x is a positively sloped line, meaning that it points to the right. It also has a y-intercept of (0,0).

y = -1/2x + 3 is a negatively sloped line, meaning that it points to the left. It has a y-intercept of (0,-3).

The correct graph is Graph A.

Hope this helps! :)

4 0
3 years ago
Please answer it’s urgent
Alika [10]
That person is correct ^
3 0
3 years ago
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