A line has a gradient of 3 and passes through the point (-3,3). its y intercept is a)0 b)3 c)6 d)9 or e) 12
Recall the point-slope form:
y - y1 = m(x - x1)
where
(x1, y1) = a point on the line
m = slope or the gradient
In the problem, we have a gradient or slope = 3, and point (-3,3) on the line.
Substituting,
y - 3 = 3(x - (-3))
y - 3 = 3(x + 3)
y = 3x + 9 + 3
y = 3x + 12
Note that this form is the slope-intercept form (y = mx + b).
In the equation we got, the slope (m) is 3, and the y-intercept (b) is 12.
Hope this helps~ :)
find the gradient which passes through (-1,5) and (3,-30
To find the y-intercept of a line, we can use the equation of a line in slope-intercept form, which is:
y = mx + b
where m is the gradient (or slope) of the line, and b is the y-intercept.
We are given that the line has a gradient of 3 and passes through the point (-3,3). We can substitute these values into the equation to find the value of b.
3 = 3(-3) + b
Simplifying the equation, we get:
3 = -9 + b
Adding 9 to both sides of the equation, we have:
3 + 9 = b
b = 12
Therefore, the y-intercept is 12.
So the answer is e) 12.
To find the y-intercept of the line, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the gradient (or slope) and b is the y-intercept.
Given that the gradient is 3 and the line passes through the point (-3, 3), we can substitute these values into the equation to solve for the y-intercept.
So, we have the equation y = 3x + b, and we know that when x = -3, y = 3.
Substituting these values into the equation, we get:
3 = 3(-3) + b
Simplifying this equation, we have:
3 = -9 + b
To solve for b, we can isolate it by moving -9 to the other side of the equation:
b = 3 + 9
b = 12
Therefore, the y-intercept of the line is 12.
Therefore, the correct answer is e) 12.