The diagram shows the straight line which passess through points (0,1) and (3, 13) Find the equation of a straight
line -

Step 1: Find the gradient/slope

Gradient and slope are interchangeable words. To find the gradient/slope we need to use two points that we know are on the line and the following formula: (y2 - y1) / (x2 - x1)

Point 1 = (0,1)

Point 2 = (3,13)

Gradient = (13 - 1) / (3 - 0)

Gradient = 12 / 3

Gradient = 4

Step 2: Find the y-intercept

We can use the slope-intercept form to find the y-intercept. To do so, we plug in the gradient and one of the points on the line. You can pick either point to plug in here!

Slope-intercept form: y = mx + b

-m is the gradient

-b is the y-intercept (that we are trying to find)

13 = 4(3) + b

13 = 12 + b

b = 1

Step 3: Put it all together in slope-intercept form

Now that we have the slope and y-intercept, all that's left to do is plug in the values.

y = mx + b

y = 4x + 1

y = 4x + 1

Hope this helps!!

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

1/6

step-by-step explanation: