Exercises 143–145 will help you prepare for the material covered in the next section. Find the ordered pairs ( ______, 0) and (0, _______) satisfying 4x-3y-6=0.

Verified step by step guidance

1. Understand that the problem asks for the x-intercept and y-intercept of the line given by the equation $\mathrm{4x}-3y-6=0$. The x-intercept is the point where the line crosses the x-axis, so the y-coordinate is 0. The y-intercept is where the line crosses the y-axis, so the x-coordinate is 0.
2. To find the x-intercept, substitute $y=0$ into the equation: $4x\; -\; 3(0)\; -\; 6\; =\; 0$. Simplify this to find the value of $x$.
3. Solve the simplified equation for $x$ to get the x-coordinate of the x-intercept. The ordered pair will be $(x,\; 0)$.
4. To find the y-intercept, substitute $x=0$ into the original equation: $4(0)\; -\; 3y\; -\; 6\; =\; 0$. Simplify this to find the value of $y$.
5. Solve the simplified equation for $y$ to get the y-coordinate of the y-intercept. The ordered pair will be $(0,\; y)$.

Key Concepts

Finding x-intercepts

The x-intercept of a line is the point where the graph crosses the x-axis, meaning the y-coordinate is zero. To find it, substitute y = 0 into the equation and solve for x, resulting in an ordered pair (x, 0).

Finding y-intercepts

The y-intercept is where the graph crosses the y-axis, so the x-coordinate is zero. Substitute x = 0 into the equation and solve for y to find the ordered pair (0, y). This point shows where the line meets the y-axis.

Solving linear equations

Solving linear equations involves isolating variables to find their values. In this context, substituting zero for one variable simplifies the equation, allowing you to solve for the other variable and find intercepts.