Question

Help please step by step

Answer 1

The equation of a straight line in slope-intercept form is y = mx + c, where m is the gradient and c is the y-intercept.

We are given that the gradient is 6 and the line passes through the point (3, 19). We can use the point-slope form of the equation of a line to find the y-intercept.

Point-slope form of the equation of a line:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope.

Using (3, 19) as the point and 6 as the slope, we get:

y - 19 = 6(x - 3)

Simplifying:

y - 19 = 6x - 18

y = 6x + 1

So the equation of the line in slope-intercept form is y = 6x + 1.

Hope this helps, have a great day :)
Summer holidays soon!

Answer 2

Step 1: Write down the formula for the equation of a straight line in slope-intercept form:

y = mx + c

where m is the gradient and c is the y-intercept.

Step 2: Substitute the given values into the formula.

The gradient m is given as 6 and the point (3, 19) is on the line. We can use this point to find the value of c.

So, we have:

y = 6x + c (substituting m = 6)

19 = 6(3) + c (substituting x = 3 and y = 19)

Step 3: Solve for c.

Using the equation above, we can simplify and solve for c:

19 = 18 + c

c = 19 - 18

c = 1

Step 4: Write the final equation.

Now that we know the value of c, we can substitute it back into the equation we found earlier to get the final equation:

y = 6x + 1

So, the equation of the line in the form y + mx + c is:

y = 6x + 1