Putting the equation in y = mx + b form we obtain y = 1.5x – 2.5.

The slope is 1.5.

This question is asking us to find the x-intercept. Remember that the y-value is equal to zero at the x-intercept. Substitute zero in for the y-variable in the equation and solve for the x-variable.

\(\displaystyle \frac{1}{2}(0)+10=6x-2\)

\(\displaystyle 10=6x-2\)

Add 2 to both sides of the equation.

\(\displaystyle 10+2=6x-2+2\)

\(\displaystyle 12=6x\)

Divide both sides of the equation by 6.

\(\displaystyle \frac{12}{6}=\frac{6x}{6}\)

\(\displaystyle x=2\)

The line crosses the x-axis at 2. 

The equation of a line can be written in the following form:

\(\displaystyle y=mx+b\) 

In this formula, m is the slope, and b represents the y-intercept. The problem provides the y-intercept; therefore, we know the following information:

\(\displaystyle b = -6\)

We can calculate the slope of the line, because if any two points on the function are known, then the slope can be calculated. Generically, the slope of a line is defined as the function's rise over run, or more technically, the changes in the y-values over the changes in the x-values.  It is formally written as the following equation:

\(\displaystyle \text{Slope}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

The problem provides the two intercepts of the line, which can be written as \(\displaystyle \left ( 4,0\right )\) and \(\displaystyle \left ( 0,-6\right )\). Substitute these points into the equation for slope and solve: 

\(\displaystyle \text{Slope}=\frac{(-6) - 0}{0-4}\)

\(\displaystyle \text{Slope}=\frac{-6}{-4}\)

\(\displaystyle \text{Slope}=\frac{3}{2}\).

Substitute the calculated values into the general equation of a line to get the correct answer: 

\(\displaystyle y=\frac{3}{2}x-6\).

The equation is already in slope-intercept form. The y-intercept is (0, –2). Plug in 0 for y and we get the x intercept of (1, 0)

The x-intercept occurs when the y-coordinate = 0.

y = –3x + 12

0 = –3x + 12

3x = 12

x = 12/3 = 4

\(\displaystyle \dpi{100} \small 4x+8=3x-7\)

\(\displaystyle \dpi{100} \small x+8=-7\)

\(\displaystyle \dpi{100} \small x=-15\)

The answer is \(\displaystyle 5\).

The slope of the line is determined by calculating the change in \(\displaystyle y\) over the change in \(\displaystyle x, (8-2)/(-4-4) = -(6/8)\).

The point-slope form of the equation for the line is then

\(\displaystyle (y-2) = -(6/8)*(x-4)\). The \(\displaystyle y\)-intercept is determined by setting \(\displaystyle x=0\) and solving for \(\displaystyle y\). This simplifies to \(\displaystyle y=5\) which shows that \(\displaystyle 5\) is the \(\displaystyle y\)-interecept.

To find the intercepts of a line, we must set the \(\displaystyle x\) and \(\displaystyle y\) values equal to zero and then solve.  

\(\displaystyle 0 = 3x +6\)

\(\displaystyle -6 = 3x\)

\(\displaystyle x = -2\)

\(\displaystyle (-2, 0)\)

\(\displaystyle y = 3 (0) + 6\)

\(\displaystyle y = 6\)

\(\displaystyle (0, 6)\)

The generic equation of a circle is (x - x₀)² + (y - y₀)² = r², where (x₀, y₀) are the coordinates of the center and r is the radius.

\(\displaystyle x^2+y^2=64\)

In this case, the circle is centered at the origin with a radius of 8. Therefore the circle hits all points that are a distance of 8 from the origin, which results in coordinates of (8,0) and (-8,0) on the x-axis.

Point-slope form follows the format y - y₁ = m(x - x₁).

Using the given point and slope, we can use this formula to get the equation y - 8 = -2(x + 5).

From here, we can find the y-intercept by setting x equal to zero and solving.

y - 8 = -2(0 + 5)

y - 8 = -2(5) = -10

y = -2

Our y-intercept will be (0,-2).