To find the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex], we start by using the given equation of the line:
[tex]\[
y = 2x - 3
\][/tex]
### Step 1: Finding [tex]\(a\)[/tex]
We know the ordered pair [tex]\((a, -1)\)[/tex] belongs to the line. Hence, substituting [tex]\(y = -1\)[/tex] and [tex]\(x = a\)[/tex] into the equation:
[tex]\[
-1 = 2a - 3
\][/tex]
To solve for [tex]\(a\)[/tex], we first add 3 to both sides of the equation:
[tex]\[
-1 + 3 = 2a
\][/tex]
Which simplifies to:
[tex]\[
2 = 2a
\][/tex]
Next, we divide both sides by 2:
[tex]\[
a = 1
\][/tex]
Thus, the value of [tex]\(a\)[/tex] is:
[tex]\[
a = 1
\][/tex]
### Step 2: Finding [tex]\(b\)[/tex]
We know the ordered pair [tex]\((5, b)\)[/tex] belongs to the line. Hence, substituting [tex]\(x = 5\)[/tex] into the equation and solving for [tex]\(y = b\)[/tex]:
[tex]\[
b = 2(5) - 3
\][/tex]
This simplifies to:
[tex]\[
b = 10 - 3
\][/tex]
Which further simplifies to:
[tex]\[
b = 7
\][/tex]
Thus, the value of [tex]\(b\)[/tex] is:
[tex]\[
b = 7
\][/tex]
### Summary
The values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are:
[tex]\[
a = 1 \quad \text{and} \quad b = 7
\][/tex]
