What is an equation of the line that passes through the points (4,-6) and has a slope of -3

Mathematics

1 answer:

Akimi4 [234]3 years ago

7 0

Answer:

1) y = -3x + 6

Step-by-step explanation:

1) First, write the equation of the line in point-slope form with the given information. Use the point-slope formula $y-y_1 = m (x-x_1)$ and substitute values for $m$ , $x_1$ , and $y_1$ .

Since $m$ represents the slope, substitute -3 in its place. Since $x_1$ and $y_1$ represent the x and y values of the point the line intersects, substitute the x and y values of (4,-6) into the formula as well. This gives the following equation:

$y+6 = -3(x-4)$

2) Now, isolate the y in the equation to put it in slope-intercept form and find the answer.

$y + 6 = -3(x-4)\\y + 6 = -3x+12\\y = -3x+6$

So, the first option is correct.

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<h2>Steps:</h2>

Vertex Form: y = a(x - h)² + k with (h,k) as the vertex

So firstly, let's start with the vertex. Since this is in vertex form, we can find the vertex easily. Since 3 is in the h variable and -4 is in the k variable, <u>the vertex is (3,-4).</u>

Next, the axis of symmetry. Remember that the vertex's x-coordinate and the axis of symmetry are the same. In this case, since the vertex's x-coordinate is 3, this means that <u>the axis of symmetry is x = 3.</u>

Next, whether the vertex is a minimum or a maximum. To determine whether it's a minimum or a maximum, we look towards the a variable of the vertex form. If a is negative, then the parabola opens down and the vertex is a maximum. However, if a is positive, then the parabola opens up and the vertex is a minimum. In this case, a = 1 and since 1 is positive, <u>this makes the vertex a minimum.</u>

Next, to find the y-intercept plug 0 into the x-variable and solve:

$y=(0-3)^2-4\\y=(-3)^2-4\\y=9-4\\y=5$

<u>The y-intercept is (0,5).</u>

Next, to find the x-intercepts plug 0 into the y-variable to solve. Since it's a bit less straightforward than finding the y-intercept, I will walk through the steps:

$0=(x-3)^2-4$