Write an equation of the line satisfying the given condition.

a) x intercept = 3 y intercept=-2

I am really not sure how to start here.

b) vertical line containing (5,-1)

Would it be y=5x-1?

c) parallel to the line 3x-4y=5 and containing the points (3,-6) .

I know that the line has to have the same slope as the one about.

d) Find the slope and y intercept of the line 4x-6y=-3

To find the y value would i plug in zero for the x and solve? And then I can find the slope?

Thank You for helping!!

a. y = 0 at the x intercept,

x = 0 at the y intercept,
Therefore: (3 , 0) , (0 , -2),

Slope = (-2-0) / (0-3) = -2/-3 = 2/3,
y = mx + b,
0 = (2/3)*3 + b,
0 = 6/3 + b,
b = -2.

Eq: y = (2/3)x -2.

b. On a vertical line, x is the same for all values of y.In other words, x is constant. On the given vertical line,x = 5. Therefore, x = 5 for all values of y:

(5 , -1) , (5 , 2) , (5 , 4). All of these points are on the required vertical line.

Eq: x = 5.

c. Given: 3x - 4y = 5, (3 , -6).
m1 = m2 = -A/B = -3/-4 = 3/4,

Y = mx + b,
-6 = (3/4)*3 + b,
-6 = 9/4 + b,
-6 -9/4 = b,
-24/4 -9/4 = b,
b = -33/4,

Eq: y = (3/4)x - 33/4.

d. Given: 4x - 6y = -3.
Slope = -A/B = -4/-6 = 4/6 = 2/3,

Let x = 0:,
4*0 - 6y = -3,
-6y = -3,
y = -3/-6 = 3/6 = 1/2 = y-intercept
.

a) To find the equation of a line with given x-intercept and y-intercept, we can use the slope-intercept form of a linear equation, which is y = mx + b.

The x-intercept is the point where the line intersects the x-axis, so it has coordinates (3, 0). The y-intercept is the point where the line intersects the y-axis, so it has coordinates (0, -2).

To find the slope (m), we can use the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line. Let's use the x-intercept and y-intercept points:

m = (-2 - 0) / (0 - 3) = -2 / -3 = 2/3

Substituting the slope (m) and the y-intercept (b) into the slope-intercept form, we get:

y = (2/3)x - 2

Therefore, the equation of the line is y = (2/3)x - 2.

b) A vertical line has an undefined slope because the line is parallel to the y-axis and does not have any horizontal change (Δx = 0).

To find the equation of a vertical line passing through the point (5, -1), we can simply write:

x = 5

Therefore, the equation of the vertical line is x = 5.

c) To find the equation of a line parallel to another line, we need to have the same slope. The given line is 3x - 4y = 5. We can rewrite this equation in slope-intercept form:

-4y = -3x + 5
y = (3/4)x - 5/4

Since the lines are parallel, the new line will have the same slope of (3/4). Now we can use the point (3, -6) to find the y-intercept (b) using the slope-intercept form:

y = (3/4)x + b

-6 = (3/4)(3) + b
-6 = (9/4) + b
-6 - (9/4) = b
-24/4 - 9/4 = b
-33/4 = b

Substituting the slope (m = 3/4) and the y-intercept (b = -33/4) into the slope-intercept form, we get:

y = (3/4)x - 33/4

Therefore, the equation of the line parallel to 3x - 4y = 5 and passing through (3, -6) is y = (3/4)x - 33/4.

d) To find the slope and y-intercept of the line 4x - 6y = -3, we need to rearrange the equation in slope-intercept form.

4x - 6y = -3
-6y = -4x - 3
y = (4/6)x + 3/6
y = (2/3)x + 1/2

The equation is now in the form y = mx + b, where m represents the slope and b represents the y-intercept. From the equation, we can identify that the slope (m) is 2/3 and the y-intercept (b) is 1/2.

Therefore, the slope of the line is 2/3 and the y-intercept is 1/2.