Question

Please help solving these questions! I’ve literally worked this for 40 mins

Answer 1

slope: -1/2
X intercepts: (6, 0)
Y intercepts: (0,3)
Equation: y=( -1/2)x + 3
Slope of the line perpendicular to the line: 2

Answer 2

Answer:

1) (6, 0), (0, 3)

2) -½

3) y= -½x +3

4) -½

5) 2

Step-by-step explanation:

1) x- intercept is the point at which the line passes though the x-axis.

From the graph, the x- intercept is (6, 0).

The y-intercept is the point at which the line passes through the y- axis.

From the graph, the y-intercept is (0, 3).

2) To find the slope, plug in the coordinates of any two points on the line into the gradient formula below.

$\boxed{slope = \frac{y1 - y2}{x1 - x2} }$

I will use the 2 points that they have provided to calculate the slope.

$slope = \frac{5 - ( - 2)}{ - 4 - 10}$

$slope = \frac{7}{ - 14}$

$slope = - \frac{1}{2}$

3) The equation of a line can be written as y= mx +c, where m is the gradient and c is the y-intercept.

Since we have already found those values in the previous questions, let's substitute them into the equation.

$y = - \frac{1 }{2} x + 3$

4) Parallel lines have the same slope.

Thus, the slope of a line parallel to the line in the graph will also have a slope of -½.

5) The product of the gradients of perpendicular lines is -1.

(gradient of perpendicular line)(-½)= -1

Gradient of perpendicular line

$= - 1 \div - \frac{1}{2}$

= 2