To determine which graph best represents the linear function $t$ with an x-intercept of $-1$ and a y-intercept of $5$, we can use the following approach:

1. Understanding the intercepts:

   • X-intercept: This is the point where the graph crosses the x-axis. Since the x-intercept is $-1$, the point on the graph will be $(-1, 0)$.
   • Y-intercept: This is the point where the graph crosses the y-axis. Since the y-intercept is $5$, the point on the graph will be $(0, 5)$.

2. Equation of the line:

   • Using the slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept, we already know that $b = 5$, so the equation starts as: $y = mx + 5$

   • To find the slope $m$, we can use the points $(-1, 0)$ and $(0, 5)$: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 0}{0 - (-1)} = \frac{5}{1} = 5$

   • Thus, the equation of the line is: $y = 5x + 5$

3. Graph characteristics:

   • The graph will have a steep positive slope (since $m = 5$) and pass through the points $(-1, 0)$ and $(0, 5)$.

Now, you can match this description with the provided graph choices (A, B, C, D) to find the correct graph.

Would you like further details on how to interpret graphs, or have any other questions?

Related Questions:

1. How do you calculate the slope of a line given two points?
2. What is the general form of a linear equation?
3. How can you graph a line using intercepts?
4. What is the significance of the slope in a linear equation?
5. How do you convert a linear equation from slope-intercept form to standard form?

Tip:

When graphing linear functions, always identify both intercepts first as they provide key reference points for drawing the graph.